Factual error: Murphy tells the story of the "Mary Celeste" all wrong. As this is a real incident, from real life, there would be no need for him to make anything up or tell it as a "tall tale", and as a professional salvage expert he would be familiar with it. The "Mary Celeste" was carrying 1700 barrels of denatured alcohol, not cotton, like he says. And she did not sail into the Mediterranean on her own to be found off Tripoli, but was discovered straight on course in the Atlantic, despite having been abandoned for some time (according to the last log entry). See http://www.straightdope.com/mailbag/mmaryceleste.html for more details.
Factual error: In the opening scene, when all the people are cut in half, one man's top half falls off his body taking his spinal cord with him from the bottom half. Surely this would have been cut in half along with the rest of his body.
Factual error: When they have discovered the gold aboard the Antonia Graza, Murphy is asked how much it is worth. He says that it might be worth 200 or 300 million (dollars). A fine ounce of gold (31.04 grams) goes for $360; thus, a kilogram of gold costs about $11,000. There are seven crates of gold. Since every single one of those can be handled by two men, they can't weigh more than, say, 150 kgs (and that's probably pushing it). Thus, the maximum amount of gold would be one ton (approximately). Given the aforementioned gold price, that'd be about 11 million dollars. Still respectable, but nowhere near the figure Murphy mentions.
Plot hole: The crew of the Antonia Graza is shown blowing off the door to where the gold is by putting an explosive on the INSIDE of the door. What was the purpose of blowing off a door AFTER going inside the door, planting the explosive, then going back out?
Revealing mistake: How is it that in the middle of a storm on the Baltic Sea the Arctic Warrior experiences no waves or rough sea? When the crew finds the ship, the water is almost as calm as a lake. (00:11:30)
Continuity mistake: When Jack ask Sean if he can talk to him alone for a minute, you see Jack lift his hand up pointing back with his thumb. Then he lowers his hand again. When it cuts you see Jack still holding his hand up. You also see Epps reaching in her pocket with her right hand, and when it cuts she is suddenly holding a cracker. (00:07:20)
Continuity mistake: In the beginning, when the crew is dividing their money, the number of beer bottles on the table increases between the shots. At first, there are a few half full bottles. Suddenly, there are a few full bottles and a few empty bottles, with no time to have drunk them. (00:06:55)
Factual error: Maritime law states that you are given a percentage of whatever you find, not the entire amount of whatever you find.
Factual error: The wire which cuts the dancing characters in half severs their torsos in a neat line a few inches below their armpits - but their arms remain intact. They should have been severed too, a few inches below the shoulder, and should fall away from their bodies separately.
Visible crew/equipment: At the beginning right before Santos sees the Graza, the Arctic Warrior is traveling on the sea. Off to the left you can make out the shape of another ship. Now why would that ship not have shown up on radar when Santos had said that the radar blip he saw was "10 miles to the NE"? (NOTE: you might have to kick your tv's video settings up a few notches in order to see this mistake but it is there plain as day.). (00:14:30)
Factual error: The Italian words/phrases that can be seen on the ship doors, billboards, etc. are very badly translated. In particular, the phrase "Veleno di attenzione" in the flashback part, in English would sound like "Poison of Attention." The correct Italian translation would be "Attenzione: Veleno" (01:07:45)